STOCHASTIC STABILITY OF DYNAMICAL SYSTEMS DRIVEN BY ´ LEVY PROCESSES

Tua A. Tamba and Yul Y. Nazaruddin

Keywords

L´evy process, stochastic stability, Lyapunov method

Abstract

This paper examines the asymptotic stability of dynamical systems that are driven by L´evy processes. A Le´vy process is a stochastic process with stationary and independent increments. It includes both Wiener and Poisson jump processes and is suitable for simultaneous modelling of small and large fluctuations in a system. In this paper, sufficient conditions for the asymptotic stability of the process’ sample paths are derived based on Lyapunov-like techniques. In particular, both the linear and non-linear representations of the process are investigated in the presented stability analyses.

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